What would be the implications to the Standard Model if the Higgs Boson hadn't been found with the LHC?
Also, if the Higgs Boson had not been found with the LHC, would it have been successfully proven as non-existent? Or would we just wait for an experiment with higher energy ranges?
Wikipedia actually has a very nice graphic with this information (which roughly agrees with what I remember hearing from people "in the know"):
The point is that there are both lower and upper bounds on the mass of the Higgs boson. The LHC should be able to cover pretty much the entire range that has not yet been searched, so if it doesn't find the Higgs, we can be fairly confident that something is wrong with the Standard Model.
Now, the question is, what could be wrong? Well, there are various possibilities. At the simple end, it's possible that there is more than one Higgs boson. The simplest possible model has only one Higgs boson, and for obvious reasons that's the model that many people are hoping is correct, but it's perfectly possible that there could be a multiplet of several Higgs particles instead. If there is more than one, I'm not sure how exactly that would change the lower and upper bounds on the mass range, but I believe that there is some possibility that if there is a Higgs multiplet, all the particles could have higher masses than we would be able to detect. (I used to know more about this but it's been a little while)
At the other extreme, it could be that the whole theoretical framework of the Standard Model is incorrect. That seems pretty unlikely, since pretty much every prediction the SM has made has turned out to be spot on (except for the presence of the Higgs, of course, but that's still an open question). There are definitely alternate theories waiting in the wings that will be receiving quite a bit more attention if the Higgs is not found.
We need a mechanism to control the scattering amplitude of two $W^\pm$ particles. It violates a "unitarity bound" when going above the TeV scale. Arguments based in unitarity of scattering diagrams -with leptons- have worked in the past, to predict the W boson itself, and to predict the Z boson (as a way to cancel a lack of unitarity if only W particles were involved in some models).
So yep, it should be in the LHC scale, or other alternative mechanism should be. Of course, such alternative mechanism could need other pieces at higher scale, even using a higgs mechanism, but then it would not be the "SM Electroweak Higgs".
